CLUSTERING IN A CONTINUUM PERCOLATION MODEL

We study properties of the clusters of a system of fully penetrable ba lls, a model formed by centering equal-sized balls on the points of a Poisson process. We develop a formal expression for the density of con nected clusters of k balls (called k-mers) in the system, first rigoro usly derived by Penrose [15]. Our integral expressions are free of inh erent redundancies, making them more tractable for numerical evaluatio n. We also derive and evaluate an integral expression for the average volume of k-mers.